Federica Piersimoni

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On the use of auxiliary variables in agricultural
surveys design

• Federica Piersimoni
• ISTAT - Italian National Institute of Statistics
• Roberto Benedetti
• University G.dAnnunzio of Chieti-Pescara,
  Italy
• Giuseppe Espa
• Universy of Trento, Italy

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Contents

• Actual situation
• Proposal
• Estimators
• Sampling designs
• Data description
• Simulation
• Analysis of the results
• Conclusions

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Actual situation
Sample units
Population units
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in sample surveys
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2001 scatter plot matrix tc1 cattle
slaughterings 2001 tc2 sheep and goats
slaughterings 2001 tc3 pigs slaughterings
2001 tc4 equines slaughterings 2001
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2000 scatter plot matrix tc10 cattle
slaughterings 2000 tc20 sheep and goats
slaughterings 2000 tc30 pigs slaughterings
2000 tc40 equines slaughterings 2000
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1999 scatter plot matrix tc19 cattle
slaughterings 1999 tc29 sheep and goats
slaughterings 1999 tc39 pigs slaughterings
1999 tc49 equines slaughterings 1999
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SCATTER PLOTS
tc1 cattle slaughterings 2001 tc2 sheep and
goats slaughterings 2001 tc3 pigs slaughterings
2001 tc4 equines slaughterings 2001
tc10 cattle slaughterings 2000 tc20 sheep and
goats slaughterings 2000 tc30 pigs
slaughterings 2000 tc40 equines slaughterings
2000
tc19 cattle slaughterings 1999 tc29 sheep and
goats slaughterings 1999 tc39 pigs
slaughterings 1999 tc49 equines slaughterings
1999
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Year 2001
Year 2000
Year 1999
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• Sampling frame N 2.211 units (enterprises) and
  
• 12 variables
• number of
• cattle,
• pigs,
• sheep and goats,
• equines
• slaughtered at the census surveys of 1999,
  2000 e 2001.
• ?

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? 2000 samples of size n 200 using as
auxiliary information the complete frame at 1999
and at 2000 to obtain estimates at 2001!
Estimates obtained through the Horvitz?Thompson
expansion estimator and the calibration estimator
(PV) by Deville and Särndal (1992)
Vector of the totals of the auxiliary variables
Distance function
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• Samples selection
• simple random sampling (SRS)
• stratified sampling (ST)
• ranked set sampling (RSS)
• probability proportional to size (?PS)
• balanced sampling
• ?PS balanced sampling   

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SRS direct estimate doesnt use
auxiliary information   ST auxiliary
information is used ex ante the strata setting
up five planned strata multivariate
allocation model by Bethel (1989).   
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• RSS original formulation
•  
• Selection SRS without reinsertion of a first
  sample of n units
• Ranking in increasing order of the n units of the
  sample with respect to an auxiliary variable x
  known for every population unit
• The interest variable y is measured on the first
  unit only
• A second SRS is drawn and ranked
• The interest variable y is measured on the
  second unit only
• .and so on till n replications.

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Ranking variable with k 1,,N, i 1,4
and t1999, 2000. For the units k ?
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?PS If y ? positive auxiliary variable x ?
selection with probability ? x. Such ex ante
probability is
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BALANCED SAMPLING and ?PS BALANCED
SAMPLING The balance constraint has been
imposed for the four variables to be estimated.
The difference between the two criteria in the
second case the constraint is imposed ex post to
?PS samples
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TOTAL
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Conclusions
It is better to impose the balance constraints
in design phase, than in ex post (cf. RMSE SRS
- RMSE BAL)
Best performances balanced ?PS selections and
?PS with calibration
a joint use of complex estimators together with
efficient sampling designs may reduce considerably
the variability of the estimates
but...
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but...
?PS and ?PS with calibration selection criteria
less robust of the others when outliers are
present
more efficient
bad performance of RSS method
forced univariate use of the auxiliary
information for the ranking setting up when
linear independence is present
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Simulated sampling distribution of the tc2
estimates in the case of pps, with calibration
estimator based on auxiliary variables of 2000
TRUE VALUE
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Simulated sampling distribution of the tc3
estimates in the case of pps, with calibration
estimator based on auxiliary variables of 1999
TRUE VALUE
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Simulated sampling distribution of the tc4 direct
estimates in the case of balanced pps, based on
auxiliary variables of 1999
TRUE VALUE
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Simulated sampling distribution of the tc2 direct
estimates in the case of balanced pps, based on
auxiliary variables of 2000
TRUE VALUE
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